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But how using 2 cables is better? Performance? Stability? Will GPU draw too much of currency and overheat?

Current, not currency.

And actually it will draw roughly the same current in both ways. But when you have 2 cables, current splits between them. When on one cable, first PCI-E connector takes combined current for both of them (via Kirchoff's Current Law). This can be problematic if you have power hungry card as it could be more than single connector can handle (connectors are known to burn with 300+ W board power consumption, 250-300 W ones could be problematic longer term). Your 670 is a bit more frugal though, so if you don't OC card heavily, you should be fine.

Since the cables are often constructed by crimping 2 wires into each pin on the first connector (one to the PSU, one to the second connector), all current for the 2 connectors (J1 and J2 here) will be flowing through the pins of the first connector (J1).

Seeing as how that's a crimped connection, I'd assume that the resistance would be even lower than that of the connection to the socket. Therefore, I wouldn't think it would be much of an issue.

My first post here. I'm sorry if this is too stupid to ask. I apologize. Does it matter if you use two cables that each have "dedicated" single-ended PCI-E connectors or if you use two cables that each have double-ended PCI-E connectors on the GPU side? I have an ASUS 1080 Ti with two 8-pin power connectors.
If this question is a waste of time, feel free to delete my account and ban me from the Internet forever. I'll go quietly.